The generation of surface plasmon resonances (SPRs) in gold-coated weakly tilted fiber Bragg gratings (TFBGs) strongly depends on the state of polarization of the core guided light. Recently, it was demonstrated that rotating the linear state of polarization of the guided light by 90° with respect to the grating tilt allows to turn the SPR on and off. In this work, we measure the Jones matrix associated to the TFBG transmission properties in order to be able to analyze different polarization-related parameters (i.e. dependency on wavelength of polarization dependent loss and first Stokes parameter). As they contain the information about the SPR, they can be used as a robust and accurate demodulation technique for refractometry purposes. Unlike other methods reported so far, a tight control of the input state of polarization is not required. The maximum error on refractive index measurement has been determined to be ~1 10(-5) refractive index unit (RIU), 5 times better than intensity-based measurements on the same sensors.